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%I #25 Aug 29 2024 22:39:30
%S 1,2,8,44,260,1556,9332,55988,335924,2015540,12093236,72559412,
%T 435356468,2612138804,15672832820,94036996916,564221981492,
%U 3385331888948,20311991333684,121871948002100,731231688012596,4387390128075572,26324340768453428,157946044610720564,947676267664323380
%N a(n) = T(3,n), array T given by A047848.
%C n-th difference of a(n), a(n-1), ..., a(0) is 5^(n-1) for n=1, 2, 3, ...
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-6).
%F a(n) = (6^n + 4)/5. - _Ralf Stephan_, Feb 14 2004
%F From _Philippe Deléham_, Oct 05 2009: (Start)
%F a(0) = 1, a(1) = 2, a(n) = 7*a(n-1) - 6*a(n-2) for n > 1.
%F G.f.: (1 - 5*x)/(1 - 7*x + 6*x^2). (End)
%F a(n) = 6*a(n-1) - 4 (with a(0)=1). - _Vincenzo Librandi_, Aug 06 2010
%F exp(x)*(exp(5*x) + 4)/5. - _Elmo R. Oliveira_, Aug 29 2024
%p a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=6*a[n-1]+1 od: seq(a[n]+1, n=0..20); # _Zerinvary Lajos_, Mar 20 2008
%Y Cf. A047848.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_
%E a(21)-a(24) from _Elmo R. Oliveira_, Aug 29 2024